Interferometers are optical instruments used for measuring surface topographies to map variations in surface height with high accuracy. Many interferometer techniques, however, require a prior knowledge of material parameters and film thickness. Moreover, interferometers, such as Scanning White Light Interferometers, suffer from low computation speed due to the number of calculations that are required to reconstruct the sample surface. In particular, analytical approaches to surface reconstruction through the use of Fourier Domain Analysis require prefiltering of the signal, followed by Fourier analysis of each data point in the image plane. In many practical applications, the Fourier Domain Analysis approach is inherently erroneous due to an insufficient description of the thin films and/or dissimilar material properties within the measured region. Likewise, empirical approaches that perform correlation to library entries which can be used to describe local film properties, must also prefilter the signal and correlate to image plane data points. Both such traditional approaches to Scanning White Light Interferometer signal processing are numerically intensive and computationally inefficient. Accordingly, improvements are desired
Another limitation of conventional techniques is the inability to efficiently measure local topography (e.g. roughness) in the presence of thin films. While a relative precise and accurate average thickness of the analyzed area may be determined with, for instance, a library search, errors in thickness for individual small areas (single data point such as a pixel in a light detector) will translate to an amplified height error in the local topography. The amplification coefficient depends on film properties (e.g. T, N&K) and can be an order of magnitude of the thickness error. The thickness error of individual data point is due to measurement system noise and traditionally requires signal averaging to reduce the noise contribution. Signal averaging, however, suffers from long measurement time preventing efficient usage, strict requirements on measurement system stability (as long measurement time is required) and low efficiency of noise suppression (as square root of N—number of averages). The improvement is, therefore, desired.